DLMF:7.7.E5 (Q2375)

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DLMF:7.7.E5
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    Statements

    Defining formula
    ∫ 0 1 e - a ⁢ t 2 t 2 + 1 ⁢ d t = π 4 ⁢ e a ⁢ ( 1 - ( erf ⁡ a ) 2 ) , superscript subscript 0 1 superscript 𝑒 𝑎 superscript 𝑡 2 superscript 𝑡 2 1 𝑡 𝜋 4 superscript 𝑒 𝑎 1 superscript error-function 𝑎 2 {\displaystyle{\displaystyle\int_{0}^{1}\frac{e^{-at^{2}}}{t^{2}+1}\mathrm{d}t% =\frac{\pi}{4}e^{a}\left(1-(\operatorname{erf}\sqrt{a})^{2}\right),}}
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    DLMF id
    DLMF:7.7.E5
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    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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